Transform coding is a compression technique used in many audio, image and video compression systems. Uncompressed digital image and video is typically represented or captured as samples of picture elements or colors at locations in an image or video frame arranged in a two dimensional grid. For example, a typical format for images consists of a stream of 24-bit color picture element samples arranged as a grid. Each sample is a number representing color components at a pixel location in the grid within a color space, such as RGB, or YIQ, among others. Various image and video systems may use various different color, spatial and time resolutions of sampling.
Uncompressed digital image and video signals can consume considerable storage and transmission capacity. Transform coding reduces the size of digital images and video by transforming the spatial-domain representation of the signal into a frequency-domain (or other like transform domain) representation, and then reducing resolution of certain generally less perceptible frequency components of the transform-domain representation. This generally produces much less perceptible degradation of the digital signal compared to reducing color or spatial resolution of images or video in the spatial domain.
More specifically, a typical transform coding technique 100 shown in FIG. 1 divides the uncompressed digital image's pixels into fixed-size two dimensional blocks, each block possibly overlapping with other blocks. A linear transform 110 that does spatial-frequency analysis is applied to each block, which converts the spaced samples within the block to a set of frequency (or transform) coefficients generally representing the strength of the digital signal in corresponding frequency bands over the block interval. For compression, the transform coefficients may be selectively quantized (i.e., reduced in resolution, such as by dropping least significant bits of the coefficient values or otherwise mapping values in a higher resolution number set to a lower resolution), and also entropy or variable-length coded into a compressed data stream by quantizer/entropy coder 120. After dequantization/entropy decoding 130, the transform coefficients will inversely transform 140 to nearly reconstruct the original color/spatial sampled image/video signal.
While compressing a still image (or an intra-coded frame in a video sequence), most common standards such as MPEG-2, MPEG-4 and Windows Media partition the image into square tiles and apply a block transform to each image tile. The transform coefficients in a given partition (commonly known as a block) are influenced only by the raw data components within the block. Irreversible or lossy operations on the encoder side such as quantization cause artifacts to appear in the decoded image. These artifacts are independent across blocks and produce a visually annoying effect known as the blocking effect. Likewise for audio data, when non-overlapping blocks are independently transform coded, quantization errors will produce discontinuities in the signal at the block boundaries upon reconstruction of the audio signal at the decoder. For audio, a periodic clicking effect is heard.
Spatial-Domain Lapped Transform
In order to minimize the blocking effect, cross block correlations can be exploited. One way of achieving cross block correlation is by using a lapped transform as described in H. Malvar, “Signal Processing with Lapped Transforms,” Artech House, Norwood Mass., 1992. A lapped transform is a transform whose input spans, besides the data elements in the current block, a few adjacent elements in neighboring blocks. Likewise, on the reconstruction side the inverse transform influences all data points in the current block as well as a few data points in neighboring blocks.
For the case of 2-dimensional (2D) data, the lapped 2D transform is a function of the current block, together with select elements of blocks to the left, top, right, bottom and possibly top-left, top-right, bottom-left and bottom-right. The number of data points in neighboring blocks that are used to compute the current transform is referred to as the overlap.
The lapped transform can be implemented in the transform domain, as a step that merges transform domain quantities after a conventional block transform. Else, it can be implemented in the spatial-domain by a pre-processing stage that is applied to pixels within the range of overlap. These two implementations are mathematically related and therefore equivalent.
As shown in FIG. 2, the spatial-domain lapped transform (SDLT) 200 is a lapped transform that is implemented as matched pre and post processing steps 210, 220 prior to the forward block transform 110, and subsequent to the inverse block transform 140, respectively. (See, e.g., Srinivasan et al., “Improvements to the Spatial-Domain Lapped Transform in Digital Media Compression,” U.S. patent application Ser. No. 10/620,744, filed Jul. 15, 2003 [hereafter “Improved SDLT Patent Application”].) The spatial-domain lapped transform is often used to retrofit existing block transform based compression techniques in order to improve efficiency.